On statistical evaluation of the linearity in assay validation

Linearity is one of the most important characteristics for evaluation of the accuracy in assay validation. The current statistical method for evaluation of the linearity recommended by the Clinical Laboratory Standard Institute (CLSI) guideline EP6-A is reviewed. The method directly compares the point estimates with the pre-specified allowable limit and completely ignores the sampling error of the point estimates. An alternative method for evaluation of linearity, proposed by Kroll et al. (2000), considers the statistical test procedure based on the average deviation from linearity (ADL). However this procedure is based on an inappropriate formulation of hypotheses for the evaluation of linearity. Consequently, the type I error rates of both current methods may be inflated for inference of linearity. To claim the linearity of analytical methods, we propose that the hypothesis of proving the linearity should be formulated as the alternative hypothesis. Furthermore, any procedures for assessment of linearity should be based on the sampling distributions of the proposed test statistics. Therefore, we propose a two one-sided test (TOST) procedure and a corrected Kroll's procedure. The simulation studies were conducted to empirically compare the size and power between current and proposed methods. The simulation results show that the proposed methods not only adequately control size but also provide sufficient power. A numeric example illustrates the proposed methods.